Quantum Hashing for Finite Abelian Groups

TL;DR

This paper introduces a generalized quantum hashing method utilizing small-bias sets to efficiently represent elements of any finite abelian group, enhancing cryptographic and computational applications.

Contribution

It presents a novel quantum hashing framework based on small-bias sets, unifying and extending existing quantum fingerprinting techniques for finite abelian groups.

Findings

Provides an optimal construction for succinct quantum representations.

Unifies quantum fingerprinting as special cases of the new hashing method.

Enables potential improvements in cryptographic protocols.

Abstract

We propose a generalization of the quantum hashing technique based on the notion of the small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for succinct quantum presentation of elements of any finite abelian group, which can be used in various computational and cryptographic scenarios. The known quantum fingerprinting schemas turn out to be the special cases of the proposed quantum hashing for the corresponding abelian group.